The maintenante plugins in the list above make the entire website unavailable as long as you are not logged in. It does not matter whether a page or a post is password protected or not. Since non-logged in users don’t see anything, you can design and manage the pages as you want.
A page set to private is only that one page is publicly inaccessible. It is only accessible when you log in. Configuring each page you create so that no one sees it is very complex. Therefore my recommendation to the maintenance plugins.
By the way, you can always test this yourself by using another browser or the private mode of your browser to access your page not logged in.